Presentation is loading. Please wait.

Presentation is loading. Please wait.

Approximating the Performance of Call Centers with Queues using Loss Models Ph. Chevalier, J-Chr. Van den Schrieck Université catholique de Louvain.

Published byLindsay Elliott Modified over 9 years ago

Similar presentations

Presentation on theme: "Approximating the Performance of Call Centers with Queues using Loss Models Ph. Chevalier, J-Chr. Van den Schrieck Université catholique de Louvain."— Presentation transcript:

1 Approximating the Performance of Call Centers with Queues using Loss Models Ph. Chevalier, J-Chr. Van den Schrieck Université catholique de Louvain

2 May 11, 2006Ph. Chevalier, J-C Van den Schrieck, UCL2 Observation High correlation between performance of configurations in loss system and in systems with queues

3 May 11, 2006Ph. Chevalier, J-C Van den Schrieck, UCL3 Loss models are easier than queueing models Smaller state space. Easier approximation methods for loss systems than for queueing systems. (e.g. Hayward, Equivalent Random Method)

4 May 11, 2006Ph. Chevalier, J-C Van den Schrieck, UCL4 Main assumptions Multi skill service centers (multiple independant demands) Poisson arrivals Exponential service times One infinite queue / type of demand Processing times identical for all type

5 May 11, 2006Ph. Chevalier, J-C Van den Schrieck, UCL5 Building a loss approximation Queue with infinite length Incoming inputs with infinite patience Rejected inputs No queues Rejected if nothing available

6 May 11, 2006Ph. Chevalier, J-C Van den Schrieck, UCL6 Building a loss approximation Server configuration –Use identical configuration in loss system Routing of arriving calls –Can be applied to loss systems Scheduling of waiting calls –No equivalence in loss systems –Difficult to approximate systems with other rules than FCFS

7 May 11, 2006Ph. Chevalier, J-C Van den Schrieck, UCL7 multiple skill example Lost calls Type Z-Calls Z Type X-CallsType Y-Calls XY X-Y X-Y-Z Building a loss approximation

8 May 11, 2006Ph. Chevalier, J-C Van den Schrieck, UCL8 performance measures of Queueing Systems: –Probability of Waiting: Erlang C formula (M/M/s system): With « a » = λ / μ, the incoming load (in Erlangs). « s » the number of servers. Building a loss approximation

9 May 11, 2006Ph. Chevalier, J-C Van den Schrieck, UCL9 performance measures of Queueing Systems: –Average Waiting Time (Wq) : Building a loss approximation Finding C(s,a) is the key element

10 May 11, 2006Ph. Chevalier, J-C Van den Schrieck, UCL10 Erlang formulas Link between Erlang B and Erlang C: Where B(s,a) is the Erlang B formula with parameters « s » and « a » :

11 May 11, 2006Ph. Chevalier, J-C Van den Schrieck, UCL11 Approximations We try to extend the Erlang formulas to multi-skill settings –Incoming load « a »: easily determined –B(s,a) : Hayward approximation –Number of operators « s » : allocation based on loss system

12 May 11, 2006Ph. Chevalier, J-C Van den Schrieck, UCL12 Approximations Hayward Loss: Where: ν is the overflow rate z is the peakedness of the incoming flow,

13 May 11, 2006Ph. Chevalier, J-C Van den Schrieck, UCL13 Approximations Idea: virtually allocate operators to the different flows i.o. to make separated systems. SxSy Sxy SxSy Sxy Sxy’Sxy’’ ++ SxSy Operators: allocated according to their utilization by the different flows.

14 May 11, 2006Ph. Chevalier, J-C Van den Schrieck, UCL14 Simulation experiments Description –Comparison of systems with loss and of systems with queues. Both types receive identical incoming data. –Comparison with analytically obtained information. analysis of results

15 May 11, 2006Ph. Chevalier, J-C Van den Schrieck, UCL15 Simulation experiments 5 Erlangs X = 3Y = n X-Y = 7 n from 1 to 10 Experiments with 2 types of demands

16 May 11, 2006Ph. Chevalier, J-C Van den Schrieck, UCL16 Simulation experiments

17 May 11, 2006Ph. Chevalier, J-C Van den Schrieck, UCL17 Simulation experiments

18 May 11, 2006Ph. Chevalier, J-C Van den Schrieck, UCL18 Simulation experiments

19 May 11, 2006Ph. Chevalier, J-C Van den Schrieck, UCL19 Simulation experiments

20 May 11, 2006Ph. Chevalier, J-C Van den Schrieck, UCL20 Average Waiting Time The interaction between the different types of demand is a little harder to analyze for the average waiting time. –Once in queue the FCFS rule will tend to equalize waiting times –Each type can have very different capacity dedicated => One virtual queue, identical waiting times for all types => Independent queues for each type, different waiting times

21 May 11, 2006Ph. Chevalier, J-C Van den Schrieck, UCL21 Average Waiting Time We derivate two bounds on the waiting time: 1.A lower bound: consider one queue ; all operators are available for all calls from queue. 2.An upper bound: consider two queues ; operators answer only one type of call from queue.

22 May 11, 2006Ph. Chevalier, J-C Van den Schrieck, UCL22 Simulation experiments

23 May 11, 2006Ph. Chevalier, J-C Van den Schrieck, UCL23 Simulation experiments

24 May 11, 2006Ph. Chevalier, J-C Van den Schrieck, UCL24 Limits and further research Service time distribution : extend simulations to systems with service time distributions different from exponential Approximate other performance measures Extention to systems with impatient customers / limited size queue

Download ppt "Approximating the Performance of Call Centers with Queues using Loss Models Ph. Chevalier, J-Chr. Van den Schrieck Université catholique de Louvain."

Similar presentations

Chapter 13 Queueing Models

Chapter 13 Queueing Models
Introduction to Queuing Theory

Introduction to Queuing Theory
Traffic and routing. Network Queueing Model Packets are buffered in egress queues waiting for serialization on line Link capacity is C bps Average packet.

Traffic and routing. Network Queueing Model Packets are buffered in egress queues waiting for serialization on line Link capacity is C bps Average packet.
Maciej Stasiak, Mariusz Głąbowski Arkadiusz Wiśniewski, Piotr Zwierzykowski Groups models Modeling and Dimensioning of Mobile Networks: from GSM to LTE.

Maciej Stasiak, Mariusz Głąbowski Arkadiusz Wiśniewski, Piotr Zwierzykowski Groups models Modeling and Dimensioning of Mobile Networks: from GSM to LTE.
Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Capacity Planning and Queuing Models.

Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Capacity Planning and Queuing Models.
Silberschatz, Galvin and Gagne  2002 Modified for CSCI 399, Royden, 2005 6.1 Operating System Concepts Operating Systems Lecture 19 Scheduling IV.

Silberschatz, Galvin and Gagne  2002 Modified for CSCI 399, Royden, Operating System Concepts Operating Systems Lecture 19 Scheduling IV.
Queueing Model 2004. 5. 29 박희경.

Queueing Model 박희경.
Nur Aini Masruroh Queuing Theory. Outlines IntroductionBirth-death processSingle server modelMulti server model.

Nur Aini Masruroh Queuing Theory. Outlines IntroductionBirth-death processSingle server modelMulti server model.
Queuing Analysis Based on noted from Appendix A of Stallings Operating System text 6/10/20151.

Queuing Analysis Based on noted from Appendix A of Stallings Operating System text 6/10/20151.
Model Antrian By : Render, ect. Outline  Characteristics of a Waiting-Line System.  Arrival characteristics.  Waiting-Line characteristics.  Service.

Model Antrian By : Render, ect. Outline  Characteristics of a Waiting-Line System.  Arrival characteristics.  Waiting-Line characteristics.  Service.
1 Performance Evaluation of Computer Networks Objectives  Introduction to Queuing Theory  Little’s Theorem  Standard Notation of Queuing Systems  Poisson.

1 Performance Evaluation of Computer Networks Objectives  Introduction to Queuing Theory  Little’s Theorem  Standard Notation of Queuing Systems  Poisson.
Performance Analysis of Wavelength-Routed Optical Networks with Connection Request Retrials Fei Xue+, S. J. Ben Yoo+, Hiroyuki Yokoyama*, and Yukio Horiuchi*

Performance Analysis of Wavelength-Routed Optical Networks with Connection Request Retrials Fei Xue+, S. J. Ben Yoo+, Hiroyuki Yokoyama*, and Yukio Horiuchi*
Single queue modeling. Basic definitions for performance predictions The performance of a system that gives services could be seen from two different.

Single queue modeling. Basic definitions for performance predictions The performance of a system that gives services could be seen from two different.
Queueing Theory: Part I

Queueing Theory: Part I
On the interaction between resource flexibility and flexibility structures Fikri Karaesmen, Zeynep Aksin, Lerzan Ormeci Ko ç University Istanbul, Turkey.

On the interaction between resource flexibility and flexibility structures Fikri Karaesmen, Zeynep Aksin, Lerzan Ormeci Ko ç University Istanbul, Turkey.
Waiting Line Management

Waiting Line Management
Waiting Lines Students should be able to:

Waiting Lines Students should be able to:
1 Queueing Theory H Plan: –Introduce basics of Queueing Theory –Define notation and terminology used –Discuss properties of queuing models –Show examples.

1 Queueing Theory H Plan: –Introduce basics of Queueing Theory –Define notation and terminology used –Discuss properties of queuing models –Show examples.
Queueing Network Model. Single Class Model Open - Infinite stream of arriving customers Closed - Finite population eg Intranet users Indistinguishable.

Queueing Network Model. Single Class Model Open - Infinite stream of arriving customers Closed - Finite population eg Intranet users Indistinguishable.
MGTSC 352 Lecture 23: Congestion Management Introduction: Asgard Bank example Simulating a queue Types of congested systems, queueing template Ride’n’Collide.

MGTSC 352 Lecture 23: Congestion Management Introduction: Asgard Bank example Simulating a queue Types of congested systems, queueing template Ride’n’Collide.

Similar presentations

Ads by Google